Abstract

A modified
predictor-corrector scheme combining with the
depth gradient method
(DGM) and the weighted average flux (WAF) method has been
presented to solve the one-dimensional shallow water equations
with source terms. Approximate solutions in the predictor step are
obtained by the DGM with piecewise-linear reconstructions in each
cell volume. The source terms can then be calculated directly by
these predicted values at the corresponding half-time step. In the
corrector step, the TVD version of the WAF method is applied to
calculate the numerical fluxes at the same half-time step for each
cell face. The accuracy of numerical solutions is shown by
applying the method to solve various test cases in both steady and
unsteady problems with and without source terms. It
shows that the numerical results are in good agreement with the
existing analytical solutions as well as experimental data in some
test cases.